A shearing interferometer is used to observe a change in phase of incident light caused by an object using displacement of interference fringes. The shearing interferometer is configured to split coherent light, such as a light beam, emitted from a light source, allow a wavefront of one light component to have a distortion caused by an object, and slightly displace the other light component to form interference fringes. Instead of light, an electromagnetic wave other than light, for example, X-rays, or an electron beam can be used.
Shearing interferometers using Talbot effect have been known. In particular, Talbot interferometry using X-rays (X-ray Talbot interferometry) has recently attracted attention.
An X-ray Talbot interferometer will now be described in brief. When X-rays from an X-ray source pass through an object, a phase of the X-rays is shifted. The X-rays passed through the object are diffracted by a diffraction grating, thus forming a first interference pattern, called a self-image, at a position at a predetermined distance from the diffraction grating. A phase shift of the X-rays caused by the object can be obtained based on a distortion in the first interference pattern caused by the object. Depending on the resolution of a detector used, however, it may be difficult to directly detect the first interference pattern because the period of fringe pattern is too small to detect the standard detector. To overcome the above problem, there has been proposed a method of forming a second interference pattern, or moire pattern having a period of approximately several hundreds of micrometers by disposing an absorption grating at the position of a first interference pattern formed, the absorption grating having almost the same period as that of the first interference pattern. A distortion in the first interference pattern can be detected indirectly by detecting the moire pattern having the period which is sufficiently large to be detected by the detector.
There are some methods (phase demodulation methods) of obtaining information (object differential phase information) about a phase shift caused by an object from a second interference pattern. An example of the methods is the Fourier transform method (refer to PTL 1). According to this method, a second interference pattern is Fourier transformed and object phase information is obtained from information associated with a region surrounding a spectrum corresponding to carrier frequencies obtained by Fourier transforming the second interference pattern.
Another typical phase demodulation method is the phase shift method (refer to PTL 2). According to this method, typically, the position of an absorption grating relative to an interference pattern is shifted by a distance corresponding to a fraction of the period of the absorption grating to shift a phase, thus changing a second interference pattern. The second interference patterns are detected in each position of the absorption grating. Object phase information is obtained based on changes as detection results. In addition, a method as a combination of the Fourier transform method and the phase shift method and any other methods may be used. In the phase shift method, the period of a second interference pattern may be greater than or equal to the size of a detector or may be infinite. Second interference patterns formed using the above-described methods are also included in moire patterns in this specification.
Since the Talbot interferometer is the shearing interferometer, primary information obtained by phase demodulation using a second interference pattern is a derivative of a phase shift of X-rays caused by an object (or information about a differential phase image of the object). Accordingly, to obtain phase information about the object, the information about the differential phase image has to be integrated. Although there are some integration methods, the information about the differential phase image can be simply integrated by sequentially adding up the information in accordance with a differentiation method.